Secretary of State Mike Pompeo opened two days of high-level talks with a senior North Korean official Wednesday night, as the Trump administration tries to establish whether there is enough common ground to proceed with a summit meeting in Singapore next month.

The discussions began with a dinner Mr. Pompeo hosted for Gen. Kim Yong Chol, who is often described as the right-hand man to North Korean leader Kim Jong Un and is making his first visit to the U.S. His arrival on Wednesday made him the highest-ranking North Korean...

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